Predicting wave velocity and stress of impact of elastic slug and viscoelastic rod using viscoelastic discontinuity analysis (Standard linear solid model)

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Abstract

The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to predict stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain. We invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the predictable stresses and velocities using viscoelastic discontinuity analysis.

Original languageEnglish
Title of host publicationProceedings of the World Congress on Engineering 2012, WCE 2012
EditorsLen Gelman, Andrew Hunter, A. M. Korsunsky, S. I. Ao, David WL Hukins
PublisherNewswood Limited
Pages64-70
Number of pages7
ISBN (Print)9789881925138
Publication statusPublished - 01 Jan 2012
Event2012 World Congress on Engineering, WCE 2012 - London, United Kingdom
Duration: 04 Jul 201206 Jul 2012

Publication series

NameLecture Notes in Engineering and Computer Science
Volume2197
ISSN (Print)2078-0958

Other

Other2012 World Congress on Engineering, WCE 2012
CountryUnited Kingdom
CityLondon
Period04/07/1206/07/12

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All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

Cite this

Musa, A. B. (2012). Predicting wave velocity and stress of impact of elastic slug and viscoelastic rod using viscoelastic discontinuity analysis (Standard linear solid model). In L. Gelman, A. Hunter, A. M. Korsunsky, S. I. Ao, & D. WL. Hukins (Eds.), Proceedings of the World Congress on Engineering 2012, WCE 2012 (pp. 64-70). (Lecture Notes in Engineering and Computer Science; Vol. 2197). Newswood Limited.